In order to support the verification and validation of computational methods and codes for the safety assessment of pebble bed High-Temperature Gas-cooled Reactors (HTGRs), the calculation of first criticality and full power initial core of the high-temperature pebble bed reactor 10 MWt (HTR-10) has been defined as one of the problems specified for both code-to-code and code-to-experiment benchmarking with a focus on neutronics. HTR-10 Experimental facility serves as the source of information for the currently designed high-temperature gas-cooled nuclear reactor. It is also desired to verify the existing codes against the data obtained in the facility. In HTR-10, the core is filled with thousands of graphite and fuel pebbles. Fuel pebbles in the reactor consist of TRISO particles, which are embedded in the graphite matrix stochastically. The reactor core is also stochastically filled with pebbles. These two stochastic geometries comprise the so-called double heterogeneity of this type of reactor. In this paper, the first criticality and the power distribution in full power initial core calculations of HTR-10 are used to demonstrate treatment of this double heterogeneity using TORT-TD and Serpent for cross-section generation. HTR-10 has unique characteristics in terms of the randomness in geometry, as in all pebble bed reactors. In this technique, the core structure is modeled by TORT-TD, and Serpent is used to provide the cross-section in a double heterogeneity approach. Results obtained by TORT-TD calculations are compared with available data. It is observed that TORT-TD calculation yield sufficiently accurate results in terms of initial criticality and power distribution in full power initial core of the HTR-10 reactor.